Question

Explain how you can find the decimal by thinking of the denominator as a 4 mental math

Answer 1

To find the decimal representation of a fraction with a denominator of 4 using mental math, you can think of the fraction in terms of quarters, since 4 is the number of quarters in a whole. Here’s how you can do it step by step:

1. **Understanding the Fraction**: Start with a fraction that has 4 as the denominator, such as \( \frac{1}{4}, \frac{2}{4}, \frac{3}{4}, \frac{4}{4} \), etc.

2. **Convert to Quarters**: Recognize that the denominator 4 means you're dividing something into 4 equal parts (quarters). For example:
- \( \frac{1}{4} \) means one quarter of a whole, which is 0.25.
- \( \frac{2}{4} \) means two quarters (or half of a whole), which is 0.50.
- \( \frac{3}{4} \) means three quarters, which is 0.75.
- \( \frac{4}{4} \) means four quarters, which equals 1.

3. **General Rule**: You can remember the following conversions:
- \( \frac{1}{4} = 0.25 \)
- \( \frac{2}{4} = 0.50 \)
- \( \frac{3}{4} = 0.75 \)
- \( \frac{4}{4} = 1.00 \)

4. **Scaling Up**: If you are working with larger numerators but still have 4 as the denominator, you can apply the same concept. For instance:
- \( \frac{5}{4} \): This is 1 quarter more than a whole (4/4), which is \( 1.00 + 0.25 = 1.25 \).
- \( \frac{6}{4} \): This is \( 1.5 \) (or \( 1 \frac{2}{4} \)), which is 1.50.
- \( \frac{7}{4} \): This equals \( 1.75 \) (or \( 1 \frac{3}{4} \)).
- \( \frac{8}{4} \): This equals 2.00 (or just 2).

Using this method, you can mentally calculate the decimal representations of any fraction with a denominator of 4 by thinking in terms of quarters and adjusting for how many complete wholes you have.